Decimal Fraction Calculator

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Understanding and converting between decimal numbers and fractions is a fundamental skill in mathematics, crucial for various fields from finance to engineering. A decimal fraction is a fraction where the denominator is a power of ten (e.g., 10, 100, 1000), but more broadly, it refers to any number expressed in decimal notation. This calculator helps you effortlessly convert between these two common representations.

What is a Decimal Fraction?

A decimal fraction is essentially a way to represent numbers that are not whole. Instead of using a numerator and a denominator, it uses a decimal point to separate the whole number part from the fractional part. Each digit after the decimal point represents a power of ten in the denominator. For example, 0.5 means 5/10, 0.25 means 25/100, and 0.125 means 125/1000.

The beauty of decimal fractions lies in their ease of comparison and arithmetic operations. However, fractions often provide a more precise representation, especially for repeating decimals like 1/3 (which is 0.333… in decimal form).

How to Convert a Decimal to a Fraction

Converting a decimal to a fraction involves a few straightforward steps:

  1. Identify the number of decimal places: Count how many digits are after the decimal point. Let's call this number 'n'.
  2. Form the initial fraction: Write the decimal number (without the decimal point) as the numerator. For the denominator, use 1 followed by 'n' zeros (which is 10 raised to the power of 'n').
  3. Simplify the fraction: Find the Greatest Common Divisor (GCD) of the numerator and the denominator. Divide both the numerator and the denominator by their GCD to reduce the fraction to its simplest form.

Example: Convert 0.75 to a fraction

  1. Decimal places (n) = 2 (for 7 and 5).
  2. Initial fraction: Numerator = 75, Denominator = 100. So, 75/100.
  3. Simplify: The GCD of 75 and 100 is 25. Divide both by 25: 75 ÷ 25 = 3, and 100 ÷ 25 = 4. The simplified fraction is 3/4.

How to Convert a Fraction to a Decimal

Converting a fraction to a decimal is generally simpler:

  1. Divide the numerator by the denominator: Perform the division operation.
  2. Round if necessary: Depending on the required precision, you might need to round the resulting decimal number.

Example: Convert 3/8 to a decimal

  1. Divide 3 by 8: 3 ÷ 8 = 0.375.
  2. The decimal equivalent is 0.375.

Use the calculator below to quickly perform these conversions.

Decimal Fraction Converter

Decimal to Fraction

Fraction to Decimal

// Function to find the Greatest Common Divisor (GCD) function gcd(a, b) { if (b === 0) { return a; } return gcd(b, a % b); } function calculateDecimalToFraction() { var decimalInput = document.getElementById("decimalInput").value; var decimalNum = parseFloat(decimalInput); var fractionResultDiv = document.getElementById("fractionResult"); if (isNaN(decimalNum)) { fractionResultDiv.innerHTML = "Please enter a valid decimal number."; return; } if (decimalNum === 0) { fractionResultDiv.innerHTML = "Fractional Equivalent: 0/1"; return; } var sign = decimalNum < 0 ? "-" : ""; decimalNum = Math.abs(decimalNum); // Handle integers if (decimalNum % 1 === 0) { fractionResultDiv.innerHTML = "Fractional Equivalent: " + sign + decimalNum + "/1"; return; } var decimalStr = decimalNum.toString(); var decimalPlaces = 0; if (decimalStr.includes('.')) { decimalPlaces = decimalStr.split('.')[1].length; } var numerator = decimalNum * Math.pow(10, decimalPlaces); var denominator = Math.pow(10, decimalPlaces); // Ensure numerator is an integer after multiplication for floating point inaccuracies numerator = Math.round(numerator); var commonDivisor = gcd(numerator, denominator); var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; fractionResultDiv.innerHTML = "Fractional Equivalent: " + sign + simplifiedNumerator + "/" + simplifiedDenominator; } function calculateFractionToDecimal() { var numeratorInput = document.getElementById("numeratorInput").value; var denominatorInput = document.getElementById("denominatorInput").value; var decimalResultDiv = document.getElementById("decimalResult"); var numerator = parseFloat(numeratorInput); var denominator = parseFloat(denominatorInput); if (isNaN(numerator) || isNaN(denominator)) { decimalResultDiv.innerHTML = "Please enter valid numbers for numerator and denominator."; return; } if (denominator === 0) { decimalResultDiv.innerHTML = "Error: Denominator cannot be zero."; return; } var decimalValue = numerator / denominator; decimalResultDiv.innerHTML = "Decimal Equivalent: " + decimalValue; }

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